Recalculating the Bogoliubov coefficients from the solutions in Phys .
Rev .
D { \bf 78 } , 103517 ( 2008 ) , we obtain the mean number of boson pairs in a uniform electric field in the global coordinates dS _ { 2 } and AdS _ { 2 } , which have the correct zero-field and zero-curvature limits , and study the vacuum persistence at one-loop .
The mean number in AdS _ { 2 } gives the lowest limit to the Breitenloher-Freedman bound in the uniform electric field , and the mean numbers in dS _ { 2 } and AdS _ { 2 } satisfy the reciprocal relation { \cal N } _ { dS } ( R,E ) { \cal N } _ { AdS } ( R,E ) = 1 under the analytical continuation of the scalar curvature R .